There's almost always a cost to liberate those U.S. dollars. One recent exception is DBS's "USA Remit."
No, absolutely no trouble "claiming." There's no claim to make; it's all handled automatically. The typical pattern is that U.S. federal marshals swoop in (with FDIC accountants) on a Friday afternoon, close the failed bank, and you're then the customer of an acquiring bank on Monday morning. If/as applicable, your debit/ATM card still works over the weekend. Moreover, if by some chance you happen to be a customer of the acquiring bank already, the FDIC makes sure that your total deposit insurance isn't reduced for at least the first 6 months.
This is absolutely ironclad U.S. government insurance, well proven since the 1930s. It works for everyone, as long as you respect the generous limit (US$250,000, more if you work with the bank to title accounts correctly).(*) It works even better than the SDIC for Singapore dollars. It's really quite remarkable.
I can personally attest to how this works. I held a CD at a U.S. bank that failed, and I kept every penny, with no action required. The federal marshals closed the bank on a random Friday afternoon. The acquiring bank converted the CD (and accrued interest to that point) to an ordinary savings account. (Some acquiring banks will continue CDs to term, with onward interest, but they're not required to do that.) On Monday morning, or at any time, I could decide whether I wanted to keep that new savings account or shift the funds elsewhere (to a more attractive CD), or some of both. Absolutely nothing was required. No claim form, no phone call, no nothing -- all automatic, all insured throughout. Even online banking continued to work, statements kept coming (new bank, new logo). Smooth as butter.
It doesn't require any "faith": foreign currency deposits in Singapore are completely uninsured! There is no SDIC, no MAS, no government, no nothing. You're on your own, and the government tells you that.
So you can get 3% U.S. federal government insured (CD Bank), 3% U.S. state insured (example), or you can (maybe) get 3% completely uninsured, and with a "liberation fee" possible at the end.
Your choice, but I think it's pretty dumb not to take one of the first deals on the table.
(*) If you're above the insurance limit (don't do that, but if), the portion of your bank deposit(s) above FDIC or NCUA insurance limits automatically turns into the #1 most senior claim against the failed bank, ahead of all other creditors and stockholders. Also, it doesn't matter what currencies you keep on deposit at a FDIC or NCUA insured institution. Unlike the SDIC, the FDIC and NCUA do not discriminate against foreign currencies. The insurance limit and insurance is U.S. dollar denominated, but any non-U.S. dollar deposits are assessed at fair market value and still insured. Yes, oddly enough the FDIC and NCUA would probably provide better (higher) insurance on Singapore dollar deposits hypothetically held at a U.S. bank or U.S. credit union than the SDIC does.